Exact and numerical solutions for diffusio-reaction equations with convection term

Esta dissertação estuda essencialmente dois problemas: (A) uma classe de equações unidimensionais de reacção-difusão-convecção em meios não uniformes (dependentes do espaço), e (B) um problema elíptico não-linear e paramétrico ligado a fenómenos de capilaridade. A Análise de Perturbação Singular e a dinâmica de Hamilton-Jacobi são utilizadas na obtenção de expressões assimptóticas para a solução (com comportamento de frente) e para a sua velocidade de propagação. Os seguintes três métodos de decomposição, Adomian Decomposition Method (ADM), Decomposition Method based on Infinite Products (DIP), e New Iterative Method (NIM), são apresentados e brevemente comparados. Adicionalmente, condições suficientes para a convergência da solução em série, obtida pelo ADM, e uma aplicação a um problema da Telecomunicações por Fibras Ópticas, envolvendo EDOs não-lineares designadas equações de Raman, são discutidas. Um ponto de vista mais abrangente que unifica os métodos de decomposição referidos é também apresentado. Para subclasses desta EDP são obtidas soluções numa forma explícita, para diferentes tipos de dados e usando uma variante do método de simetrias de Bluman-Cole. Usando Teoria de Pontos Críticos (o teorema usualmente designado mountain pass) e técnicas de truncatura, prova-se a existência de duas soluções não triviais (uma positiva e uma negativa) para o problema elíptico não-linear e paramétrico (B). A existência de uma terceira solução não trivial é demonstrada usando Grupos Críticos e Teoria de Morse.

Photodynamic inactivation of bacteria by cationic porphyrins : their cellular targets and potential environmental applications

Photodynamic inactivation (PDI) is defined as the process of cell destruction by oxidative stress resulting from the interaction between light and a photosensitizer (PS), in the presence of molecular oxygen. PDI of bacteria has been extensively studied in recent years, proving to be a promising alternative to conventional antimicrobial agents for the treatment of superficial and localized infections. Moreover, the applicability of PDI goes far beyond the clinical field, as its potential use in water disinfection, using PS immobilized on solid supports, is currently under study. The aim of the first part of this work was to study the oxidative modifications in phospholipids, nucleic acids and proteins of Escherichia coli and Staphylococcus warneri, subjected to photodynamic treatment with cationic porphyrins. The aims of the second part of the work were to study the efficiency of PDI in aquaculture water and the influence of different physicalchemical parameters in this process, using the Gram-negative bioluminescent bacterium Vibrio fischeri, and to evaluate the possibility of recycling cationic PS immobilized on magnetic nanoparticles. To study the oxidative changes in membrane phospholipids, a lipidomic approach has been used, combining chromatographic techniques and mass spectrometry. The FOX2 assay was used to determine the concentration of lipid hydroperoxides generated after treatment. The oxidative modifications in the proteins were analyzed by one-dimensional polyacrylamide gel electrophoresis (SDS-PAGE). Changes in the intracellular nucleic acids were analyzed by agarose gel electrophoresis and the concentration of doublestranded DNA was determined by fluorimetry. The oxidative changes of bacterial PDI at the molecular level were analyzed by infrared spectroscopy. In laboratory tests, bacteria (108 CFU mL-1) were irradiated with white light (4.0 mW cm-2) after incubation with the PS (Tri-Py+-Me-PF or Tetra-Py+-Me) at concentrations of 0.5 and 5.0 μM for S. warneri and E. coli, respectively. Bacteria were irradiated with different light doses (up to 9.6 J cm-2 for S. warneri and up to 64.8 J cm-2 for E. coli) and the changes were evaluated throughout the irradiation time. In the study of phospholipids, only the porphyrin Tri-Py+-Me-PF and a light dose of 64.8 J cm-2 were tested. The efficiency of PDI in aquaculture has been evaluated in two different conditions: in buffer solution, varying temperature, pH, salinity and oxygen concentration, and in aquaculture water samples, to reproduce the conditions of PDI in situ. The kinetics of the process was determined in realtime during the experiments by measuring the bioluminescence of V. fischeri (107 CFU mL-1, corresponding to a level of bioluminescence of 105 relative light units). A concentration of 5.0 μM of Tri-Py+-Me-PF was used in the experiments with buffer solution, and 10 to 50 μM in the experiments with aquaculture water. Artificial white light (4.0 mW cm-2) and solar irradiation (40 mW cm-2) were used as light sources.